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This is the best explanation of the eigenthings in my opinion. Too many people, this article included, reach for more advanced concepts to explain something as simple as "eigenvectors are how an operator transforms stuff and eigenvalues are how much."

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Thank you - its too easy to get into the weeds with mathematics and lose the "why" of something. Connecting these higher level concepts with the algebra that _most_ people have experience with ends up being a more direct way to share knowledge vs diving into the higher level stuff that enthusiasts really enjoy.

God knows how I passed 4 years of engineering math without ever being able to describe to anyone what eigen* actually are, but I think that's actually the norm.

That's completely normal and very unfortunate. I only learned about the geometry of the eigen*s from an EE professor who loved math.

Unfortunately, the history of the eigen*s is rooted in the opaque and cryptic (but rigorous) linear algebra definition, and the non-rigorous but meaningful geometry came later.

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